Question

ABCD is a square if it's one diagonal is 30✓2 m then , it's perimeter is ______. ​

Answer 1

Answer:

120m

Step-by-step explanation:

The relation between the side of a square and it's diagonal is diagonal length=√2Xside length

Answer 2

Answer:

• Perimeter of square is 18.395 m².

Step-by-step explanation:

Given:-

• ABCD is a square.
• One diagonal of square ABCD is 20√2 m.

To find:-

• Perimeter of square.

Solution:-

Concept:-

• We will find any one side of square for perimeter. Our first motive will be to find side.

Let, diagonal BD length be 30√2 m.

And Let sides of triangle be x. [We know all sides of square are equal and parallel.]

• We know all angles of a square is 90° .

∴ ∠C = 90°

• We have diagonal BD and Angle to be 90°. So, ∆BCD will be right angle triangle.

∴ ∆BCD is right angle triangle in which BD is Hypotenuse, CD is base and BC is Perpendicular.

According to Pythagoras theorem

Hypotenuse² = Base² + Perpendicular²

Hypotenuse = 30√3 m

Perpendicular = Base = x [∵ Base and Perpendicular of triangle are sides of square and all sides of square are equal]

Put the values of hypotenuse, perpendicular and base in Pythagoras theorem,

➝ x² + x² = 30√2

➝ 2x² = 30√2

➝ x² = 30√2/2

➝ x² = 15√2

• √2 is irrational number and √2 = 1.41.

➝ x² = 15 × 1.41

➝ x² = 21.15

➝ x = √21.15

➝ x = 4.59 (approx)

Base and perpendicular are sides of triangle and sides of square as well.

We have taken base and perpendicular be x. So, Base is 4.59 m and perpendicular is 4.59 m. So, One side of square is 4.59 m.

Perimeter of square = 4 × side

= 4 × 4.59

= 18.395

Therefore,

Perimeter of square is 18.39 m² (approx).